Question

The area of a rectangular garden is 336 square meters. The width is 2 meters longer than 1/2 of the length. Find the length and the width.

Answer 1

width=(1/2)x+2 where x is the length
336=x*((1/2)x+2)
336=(1/2)x^2+2
668=x^2
x=sqrt(668)
I think?

Answer 2

Sorry DiSc02, I need the length and width.

Answer 3

Let L and w be the length and width respectively.
\[\left\{L w=336,w=\frac{L}{2}+2\right\} \]\[\{L=24,w=14\} \]

Answer 4

I solved it. The length is 24 and the width is 14

Answer 5

lol thanks Robtobey I got the same answer

Answer 6

let the length be x metres
therefore
\[width = \frac{1}{2}\times x +2\]
Area of rectangular garden = length *width
i.e. \[336 = x \times ( \frac{1}{2} x + 2)\]
\[336 = x \times \frac{1}{2}(x + 4)\]
\[336 \times 2 = x \times (x + 4)\]
\[672 = x^2 + 4x \rightarrow x^2 + 4x -672 =0\]
\[x^2 + 28x -24x -672 =0 \rightarrow x(x+28)-24(x+28) =0\]
\[\rightarrow (x+28)(x-24)=0\]
i.e. (x+28)= 0 or (x-24)=0
i.e. x= -28 or x= 24
but -28 cannnot be the length as it is a negative number
Hence x= 24 is the length of the rectangular garden
Therefore
Width = \[Width = \frac{1}{2} \times 24 + 2 = 12 + 2 = 14 units\]
Hence length is 24 units and width is 14 units
@Tfreeland88

Answer 7

Thank you for all your work dpasingh!

Answer 8

@Tfreeland88 Medal please.

Answer 9

How do I do that?

Answer 10

just click on the best response button beside my name

Answer 11

Oh, someone had it before you, is there a way to still reward you?